You can use a floor sander if the deck is that bad. Go across, then diagonal then with the grain. Make sure the nails are below the surface so you don't tear the sandpaper. Pop them down a bit with a punch if they are up, or screw a tad deeper if they are screws. Be careful with the floor sander and go easy because it's heavy duty and can dig in. Stay smooth, go easy and the deck will be smooth.
Let the new surface weather a few rains, then clean it with a wood cleaner to get any mildew, algae growth and then follow up with an oxalic acid. (deck brightener) to rid tannin stains, rust stains from nails..etc. These products are usually diluted, read the directions and be cautious with the brightener. Wear gloves, goggles, etc. Careful with splashing yourself.
Let it dry for 2 days and put the stain on later in the day so it doesn't flash dry before it absorbs. Wipe it down 15 minutes later to get the shiny spots off and you got yourself a new deck.

A big.. P.S!... Your deck may be pressure-treated and sanding this stuff is toxic. Make sure you close all the doors and windows of your house, wear a mask, goggles, etc. Put the pets and kids in so they aren't breathing this stuff and clean it up the best you can when you're done. Shop vac the dust up on the deck, on the grass, etc.
I don't want to alarm you just be careful in how you do this that's all.

basset,

Like gorrillabuilder said, make sure those screws/nails are recessed! If not, the heads will shred your sand paper.

Nothing will "restore" a severely weathered deck better than a drum sander.

I buy all my sand paper from www.supergrit.com. Good prices. They can a full assortmant of sandpaper for floor (drum) sanders too. I imagine that you will want to start out with something agressive like 80 grit and finish (parallel to the grain) with something like 220.

Thanx folks. I'm going to give it a try. A good way for the kids to earn their keep over the summer - A nickle a for each nail set.

Again, thanx to all.
Keith

careful with the high grain of sandpaper.. if you make it too tight it won't absorb stain.. 60-80 should be enough.

it will absorb, but won't adhere as much ......i mean.

(eavesdropping) are you saying the last pass should be just 60 or 80 grit?

Celtic, I never go above 60 grit.

Thanks for the post,I was looking for the same info.

Basset, I have the same situation. The planks are not rotten but are old, slightly twisted in places and uneven. They've probably been painted several times over the years. Did you proceed with the floor sander and how did it work out? I tried a hand sander on my old deck a few years ago, and it did nothing as far as leveling the adjacent planks to the same height.